In order to minimize the mutual coupling between sensors, a kind of co-prime nested array with adjustable element spacing is proposed. The proposed array consists of two nested arrays with different element spacing and the smallest unit intervals of two sub-arrays are determined by any two co-prime positive integers. As long as the positive integers is enough big, the smallest unit intervals of each sub-array can be far more than half -wavelength of incident signal. Hence, the mutual coupling effect between sensors can be reduced to a negligible level. Then, in order to eliminate the direction ambiguity caused by large element spacing, by using the fourth-order cumulants of received data, a direction of arrival (DOA) estimation algorithm without direction ambiguity is proposed. Compared with some classical self-correcting decoupling methods, the proposed algorithm has a higher angle resolution and estimation. Simulation results can prove the improved performance of proposed algorithm.